Woakes was part of the England squad that played in the first three matches of the series while the 21-year-old Curran will be making his Ashes debut.
Australia have retained the Ashes by winning the fourth Test at Old Trafford to take a 2-1 lead in the series. England will now be looking to avoid a first series loss against Australia at home in Tests since 2001.
England playing XI: Joe Root (c), Jofra Archer, Jonny Bairstow (wk), Stuart Broad, Rory Burns, Jos Buttler, Sam Curran, Joe Denly, Jack Leach, Ben Stokes, Chris Woakes.